Question

The perimeter of a triangular garden is 78 feet .

Answer 1

Given:

The perimeter of the garden is 78 feet

Middle length side is 4 feet greater than twice the length of the smaller side.

Longest side is 4 feet less than 3 times the length of the smallest side.

To find:

Find the length of the middle side, small side and longest side.

Let x,y and z be the length of the small side , middle side and longest side.

`\begin{gathered} y=2x+4\ldots\text{ (1)} \\ z=3x-4\ldots\text{ (2)} \end{gathered}`
`\begin{gathered} \text{Perimeter of the garden=78} \\ x+y+z=78 \\ x+2x+4+3x-4=78 \\ 6x=78 \\ x=13 \end{gathered}`

Substitute the values of x in equation(1) and equation(2) to get the values of y and z.

`\begin{gathered} y=2(13)+4 \\ y=26+4 \\ y=30 \end{gathered}`
`\begin{gathered} z=3(13)-4 \\ z=39-4 \\ z=35 \end{gathered}`

Length of the smallest side is 13 feet

Length of the middle side is 30 feet

Length of the longest side is 35 feet